Problem: Reduce to lowest terms: $- \dfrac{2}{9} \div \dfrac{8}{9} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{8}{9}$ is $ \dfrac{9}{8}$ Therefore: $ - \dfrac{2}{9} \div \dfrac{8}{9} = - \dfrac{2}{9} \times \dfrac{9}{8} $ $ \phantom{- \dfrac{2}{9} \times \dfrac{9}{8}} = \dfrac{-2 \times 9}{9 \times 8} $ $ \phantom{- \dfrac{2}{9} \times \dfrac{9}{8}} = \dfrac{-18}{72} $ The numerator and denominator have a common divisor of $18$, so we can simplify: $ \dfrac{-18}{72} = \dfrac{-18 \div 18}{72 \div 18} = -\dfrac{1}{4} $